where \( \omega _j= \omega _{j} (\tau _j)\) , \(\eta _j=\eta _j(\tau _j)\)  and \(\beta _j=\beta _j(\tau _j)=[\beta _{1j},..., \beta _{Kj}]^{\prime }\)  are model parameters that depend on the chosen level \(\tau _j\)  and where we suppress the index \(\tau _j\)  for simplicity of notation.
The dynamic specification in (REF ) is well-known in the literature as the CAViaR model of [1]}, which attempts to compute the \(\tau \) -th level VaR by estimating the \(\tau \) -th level quantile of the asset returns through a conditional autoregressive structure.
The function \(\ell (\cdot )\)  blackrepresents the so-called News Impact Curve (NIC), originally introduced by [2]}. For each \(j\) -th component, the NIC function essentially feeds back the last available observation (\( Y_{t-1j}\) ) into the present value of the conditional quantile, through the \(K \times 1\)  parameter vector \(\beta _j\) . Following the CAViaR literature, we will consider different specifications for \(\ell (\cdot )\)  to model the marginal quantiles, blackwhich will be described in the next section.
